cp's OEIS Frontend

A247585 Period of the decimal expansion of 1/p as p runs through the prime numbers of the form n^2+1 (0 by convention for the primes 2 and 5).

%I A247585 #17 Oct 20 2024 03:53:04
%S A247585 0,0,16,3,4,98,256,200,576,338,1296,200,1458,3136,242,1369,7056,1620,
%T A247585 4418,12100,13456,3600,15376,567,3380,8978,10658,7500,24336,25,5780,
%U A247585 30976,600,33856,41616,10609,44100,50176,52900,55696,14400,62500,65536,33800,69696,8100
%N A247585 Period of the decimal expansion of 1/p as p runs through the prime numbers of the form n^2+1 (0 by convention for the primes 2 and 5).
%C A247585 Subsequence of A002371 or period of the decimal expansion of 1/A002496(n).
%C A247585 The squares > 0 in the sequence are 4, 16, 25, 256, 576, 1296, 1369, 3136, 3600, 7056, 8100, 10609, ...
%F A247585 a(n) = A002371(A000720(A002496(n))). [Corrected by _Georg Fischer_, Oct 19 2024]
%e A247585 a(3) = 16 because A002496(3) = 17 and 1/17 = 0. 0588235294117647 0588235294117647 ... has period 16.
%t A247585 lst={};Do[If[PrimeQ[n^2+1],AppendTo[lst,n^2+1]],{n,1,1000}];Table[Length[RealDigits[1/lst[[m]]][[1,1]]],{m,1,60}]
%Y A247585 Cf. A000720, A002371, A002496, A060282, A175550.
%K A247585 nonn
%O A247585 1,3
%A A247585 _Michel Lagneau_, Sep 20 2014